The Power of Two: Two Tips for Mathematicians

Every person I know, even mathematicians, have their favorite numbers. Mine used to be 13, because I liked being contrarian. Then I switched to 17 because it was the seventh prime number and I also liked 7. But what is so special about the number 2? Of course, it is the only even prime, but what else?

If you did not know before, you might be interested to learn (from Wikipedia) that 2 is the only number x such that the sum of all the reciprocals of the powers of x equals x. Wikipedia will also tell you that “powers of two are central to the concept of Mersenne primes, and important to computer science.” There are even interesting things to learn about the power of two in poetry. But why should readers of the e-Mentoring Network blog care?

On these blog pages, readers will find personal success stories to learn from and thoughtful essays chock-full of solid advice. My goal writing here has been a lot more modest. From the beginning, I have tried to share things I have learned from the vast literature about productivity and then personally tried to implement into my own idiosyncratic life. In my first post here, I wrote about writing things down, how “getting things out of your head and into a trusted system” can be helpful. Then I wrote about how making a plan for your summer as you ease into it might be a good idea. Finally last summer I wrote about digital organization. Along the way I also wrote a little post about giving math talks and there too I have tried to share what I learned from others and what seems to work well for myself (whenever I can get myself to listen to myself!)

So this post is about two great tips involving the number 2 that I learned along the way. They will perhaps not double your happiness or fortune, but I promise you that you will not regret it if you do decide to take them along for the ride.

Here is the first one: The Two-Minute Rule. I learned this from David Allen’s famous book Getting Things Done, but it is easy to learn it independently of his program. The rule is quite simple:

If you find something on your to-do list that you could do in two minutes, just do it!

Of course this works well if you have a to-do list, but it can be applied to many other contexts. So here are some corollaries:

Corollary 1. If you are going through your email inbox and you see some emails that are easy to answer quickly (and, this is absolutely essential, only if they are worth answering), then go ahead and respond.

Corollary 2. If you have to print out some handouts for your class that you have already prepared, just go ahead and print when you remember to.

Corollary 3. If you need to go to the bathroom, just go!

(Ok, maybe the last one there did not need to be included, but some of us need to be occasionally reminded of this! This and “You should go and fill up your water bottle when it is empty.”)

What is the point of the two-minute rule? It is simple: It clears your inbox, it clears your to-do list, it helps you move forward, and it makes you feel good about yourself. That is a handful of points all at once. But there is more.

The two-minute rule also trains your mind to look at tasks on your list in a time-sensitive way. You learn eventually to think more carefully about how much certain types of tasks will take you. This is amazingly helpful when you are thinking of taking on new tasks. You might find that you just have too much on your plate already. Wouldn’t that be a good thing to notice before you take on more?

Alright, time to move on to the second tip invoking the special powers of 2: To rhyme with the first one, I will call this The Two-Week Rule. Here it goes:

When you receive a revise-and-resubmit request from a journal about your paper submission, turn it around in two weeks.

Sometimes this may mean that you will be dropping some of the other balls on the air to the ground, but it will only be temporary. And once you do turn that paper around in two weeks, you will feel so great! And yes, it is almost always doable. Ok, if you were asked to incorporate a new semester’s worth of data to the paper, then maybe not so much. But often the requests are much more minor than that. Even when the referees are asking for “major revision”, you can often take care of it in two intense weeks.

I have used this tip myself with much success. Each time I have received feedback, even some that I was quite unpleased with, I gave myself one whole day to fume and bicker, and then I started the clock. Literally. Once I actually counted the total number of minutes it took me to handle a set of referee reports. I have seen that it has taken me about twenty-four hours. That is one full day, but spread over a couple weeks, it is not that bad. And in the end, you can still keep the “submitted” tag on your CV for that paper until it is accepted!

I have to admit that I do not do this all the time. In fact there is a paper that is still sitting in the depths of my computer filing system waiting to be revised. My defense: the four referees each requested that I do something totally contradictory to the others’ requests. So I basically gave up. But was that wise of me? No. I do believe in the paper, so I should get my act together and take care of it. And after writing this post, now we all know that I have to do it in two weeks. What do you think? Can I?

Gizem Karaali is associate professor of mathematics at Pomona College and a founding editor of the Journal of Humanistic Mathematics. She is also an associate editor of the Mathematical Intelligencer and of Numeracy. Follow Gizem at @GizemKaraali_.

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New year, same goal: more research

I began the academic year with a renewed hope that this year would be different: that I would be smarter in how I allocated my time so as to focus on research and that I would be steadfast in my approach to saying no to the things that do not directly support this goal. Yet seven weeks have passed since the start of the spring semester and as I reevaluate and make a list of the goals I want to accomplish by the end of this academic year, I noticed that this list contains some of the same research items I aimed to complete by the end of the fall semester.

Let’s be honest: things come up. There are many additional expectations, responsibilities, and opportunities in this profession aside from our teaching and research duties. So how can we properly allocate our time to achieve our goals as researchers? Here are a few things that come to mind, along with some advice I have received along the way.

Foster Collaborations. In my last blog I wrote about building research collaborations and how I have made great friends along the way. Another great benefit of collaborative projects is the higher level of productivity. When working with others you can approach problems from a variety of perspectives, which can lead to finding the breakthrough needed to finish the results. As a research group member, I feel accountable for the part of the work I am to contribute to the project. I understand that others are counting on me, and this expectation forces me to focus on the project much more than I would if I only had myself to report to. Which leads naturally to the next point:

Involve students in your research. Last academic year I supervised three undergraduate thesis students. I had to spend time on my research in order to be prepared to discuss that week’s topic with them. These projects resulted in two publications and multiple conference presentations. Having involved my students in my research kept me motivated and excited about my work. I highly recommend other junior faculty include students in their research.

If your teaching load prohibits supervising projects during the academic year a great option is to apply for a CURM mini-grant. This grant provides faculty funds for a course buy-out, and a stipend for the student researchers. If you would prefer to work with students during the summer, but your school does not have an REU site, consider applying for the MAA National Research Experiences for Undergraduates Program. This program provides “stipends for faculty researchers and local minority undergraduates, as well as costs for student room and board for a period of six to eight weeks.”

Learn to say no. I will get this off my chest: As a Project NExT fellow (shout out to my Silver Dot 2012 cohort!) Professor Joe Gallian taught us to say yes to every opportunity so that we would find our niche within the mathematical community. His advice has lead to some great career opportunities that would not have materialized had I declined to help/participate. However, there is a point beyond which we overcommit ourselves and are therefore less productive and effective in our research endeavors. A mentor once told me that a good way to respond to requests that might not support one’s research goals, especially for pre-tenure faculty, is to say “Let me talk to my advisor/chair/suppervisor about this and I will get back to you soon.” This gives you adequate time to think about how this new commitment supports your goals, and keeps your advisor/chair/suppervisor informed on the work you are thinking of undertaking.

Ask for help. When you’ve said yes to too many things, nothing is more powerful than finding help. For example, I started a speaker series in my department and the first few years I did everything myself: inviting speakers, dealing with the necessary paperwork, finding funding sources, etc. However, this year, I reached out to my fellow civilian colleagues and asked if they would codirect the series with me. Three said yes and now the workload is divided among four. This makes the organization more manageable, and, more importantly, considerably more students are attending the lunchtime talks as a result of our teamwork. Another benefit of working with others is that the series will continue even after I leave. This is something I am quite proud of and something that would not have occurred had I not asked for help from my colleagues.

Get organized. Being able to find things is a challenge for me. My desk is always clean, but as one of my old office mates pointed out, it is because I stuff my desk’s drawers full of papers. Professor Gizem Karaali has contributed a wonderful blog about organization basics for mathematicians. It can all start with an empty email inbox! Read her article and do your best to stay organized and get an early start to your spring-cleaning.

What else do you do to stay focused on achieving your research goals? Feel free to share your tips and tricks in the comments.

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Are you thinking of working in industry?

Written by Sharon Arroyo ( and Les Button (

Opportunities in industry for people with hard-core mathematical skills can be very rewarding. In this article, we give our perspective on how to search for a job in industry. We first discuss how to match your skills and career goals with a role. We then give information about the job search, and finally point you to a resource concerning interviewing.

The first order of business is to consider what type of working environment suits you. Your ideal working environment will likely evolve over time, but this information will help frame your initial job search. For example, you might consider the following questions: Continue reading

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The importance of having a network of mentors and reaching out to all of them

(Originally posted on October 30, 2015)
We should not just reach out to our mentors when we have career- or academic-related questions but also when we may have a more personal issue and need the guidance and reassurance of individuals that have a different perspective. We don’t just need one or two mentors but an entire army of mentors at our fingertips that we can call on, especially in a moment of urgency. A few weeks ago, I was overwhelmed trying to help various individuals at critical points in their academic careers who sought out my advice and guidance, including my teenage son. While I wanted to do everything I could to help all these individuals and provide them with the best possible advice, I did not have a good perspective on certain topics to do this for all them. In particular, I did not feel I had a complete perspective when it came to helping my son decide on the particular colleges to which he should apply and my graduate mentee find a graduate program more in line with his passion.

My mentee is interested in an area that I am not familiar with and thus I had a very hard time coming up with programs that would be a good match for him and that would allow him to thrive. After thinking of various graduate program possibilities and not being able to come with any good leads, I decided to email some very well-connected individuals who would help me come up with appropriate programs and individuals with whom to connect my student. To my surprise the names of individuals they gave me as potential individuals that had a very good program for my student, with the exception of two names, were individuals I knew (not from my discipline but rather from other academic venues and service I have done). One was even a very good friend and collaborator in some work I did a few years ago. So it was very easy to reach out to them and to connect my mentee with these individuals. Since I personally knew these individuals I could even offer him some perspective on these individuals based on my interactions with them. While I knew the individuals, I would not have been able to identify these possibilities and leads for my mentee if I had not reached out to my mentors who are very connected in non-mathematical disciplines and who have daily interactions with many individuals. It is funny how we forget how well-connected we are and the resources we have within our reach through our mentors.

Given my son’s academic interest, I wanted to encourage him to apply to a particular college but I was not sure if this would be a good fit for him given that I did not know much about the culture of the institution and the particular department he was interested in. I did not want to sell a place to him based on my limited knowledge and what I perceived his experience would be if he ended up there. I was stressed and unsure of how much to encourage him when my sister said, “You are a professor. Don’t you know other professors that know that place very well and that can give you some perspective?” I did know some excellent friends and mentors who knew this place very well and its current culture, but for some reason, I had not considered this possibility. Unconsciously I probably thought “well, I am a faculty who has mentored many students and the mother of this kid, so I should be able to mentor and advise him on my own without any problem.” But I did not know this place and thus could not honestly give him the best perspective possible. However, I had four mentors who knew the place intimately and could provide me with different perspectives that I could then communicate to my son.

These mentors not only gave me perspective in regards to the school but also provided very personal views and advice. They put me at ease and made me realize that this is why we need to have multiple mentors and why we need to reach out to our army of mentors. This is true even when it is not necessarily career advice that we are seeking and when it is not necessarily us who are seeking the advice and mentoring.

Through these experiences I gained a better appreciation for the multiple and diverse set of mentors I have. I also realized that if I am to do the best I can when it comes to mentoring others, I need to keep in mind the embeddedness of mentoring such that I, as one mentor, can reach out and connect my mentees to many other mentors and give them multiple perspectives via the perspective of my own mentors. I have to remember to reach out to my army of mentors and continue to nurture and develop my mentoring network so that I will always have mentors regardless of the challenge, questions, or issues I am facing.

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Some suggestions for revising rejected grant proposals

Getting grants for research projects is hugely important for all active investigators.  In universities where research is emphasized, pre-tenure faculty will be evaluated a couple of times before the tenure decision and grant activity is an important element in that decision. Tenured faculty who aspire to be promoted to full professor must provide evidence that their work is valued nationally or internationally and one of the indicators is the grant awards. Additionally, external funding allows faculty to collect summer salary, travel to conferences, pay for collaborators’ visits, and support students. In institutions mostly dedicated to teaching mathematics, research or training grants are also important for student projects and course development.

This blog post is not about how to write a successful proposal, for which there are many resources available (see below). This post is about what to do after you are notified that your proposal did not get funded. Continue reading

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Experiencing the SACNAS conference

This post is written with contributions from graduate students Megan Ly (Megan.Ly@Colorado.EDU) and Alexander Diaz (

The SACNAS annual conference took place at the end of October this year near Washington DC. SACNAS stands for the Society for Advancement of Chicanos/Hispanics and Native Americans in Science and its mission is to foster the success of Chicano/Hispanic and Native American scientists – from college students to professionals – to attain advanced degrees, careers, and positions of leadership. The SACNAS National Conference motivates, inspires and engages participants to achieve their highest goals in pursuing education and careers in STEM fields, and mathematics is always well represented. The conference is largely dedicated to support students through scientific talks, professional development sessions, recruitment by exhibitors and long-lasting mentoring. Below are the reflections of two graduate students, Megan Ly and Alexander Diaz, who attended as evidence of what SACNAS does for students. I urge undergraduate and graduate students, especially from minority groups, to consider attending future SACNAS meetings.  Continue reading

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Building a Research Army

I am what the math community calls a young mathematician (although my grey hair disagrees wholeheartedly!) and I am often looking for new and interesting math to work on. Last calendar year was particularly fruitful in this endeavor, as I had no teaching responsibilities at West Point and was able to focus on my research. So I hope that other young mathematicians might benefit from some of my lessons learned in building a research army.

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Back to School: Universal Mentorship

This is the only time of year when I think folks on the quarter system, as opposed to semesters, have it easy. We’re in our second week of classes at Mudd, and even for those still savoring their last refreshing sip of summer, it is most definitely Back to School season. It’s in the air. I’m also returning to Mudd from sabbatical, so it’s a great opportunity for me to take stock and think deliberately about the upcoming school year.

I’m starting this year convinced that mentorship is universal. Mentorship isn’t a map with a specified domain and codomain. There isn’t a fixed group of mentors or mentees. Our roles may be fluid, and everyone is a candidate for both giving and receiving mentorship; it is universal. Below the fold, I’ll describe my experience at PCMI this summer and how it reinforced my understanding of the universal nature of mentorship.

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Mentorship and Gender

Thanks to Greg Martin for this guest post! Greg has been writing interesting and important material recently concerning gender inequity in mathematics. For the eMentoring network, he writes about mentorship and gender. What follows are Greg’s words.

Mentorship and Gender

Personal, dedicated mentorship is an extremely important part of postgraduate education and the academic career. So are mentor-like networks of more senior members of the discipline, as well as supportive networks of academic peers. Those who don’t have adequate access to these resources are at a significant disadvantage, even with full use of “official” resources such as courses and job postings. In an extreme case, a position might not even be officially publicized before being offered to the student of a close colleague. At the very least, consultation with someone who has broader experience and academic success can help an up-and-coming mathematician to optimize their allocation of energy.

Unfortunately, these mentorship opportunities are not equally available to everyone in mathematics; in particular, there is a systemic bias against female students and mathematicians. Implicit biases cause us (all of us) to systematically undervalue women in mathematics – female applicants to graduate school, female speakers at conferences, female authors of papers, female faculty members being evaluated for tenure. In particular, they cause us to be less likely to devote our time to mentoring women. Continue reading

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What can I do this summer to be ready to start a PhD program in the fall?

Congratulations to those students who have been accepted to a PhD program in the mathematical sciences starting in the fall! You are about to start an unforgettable part of your life. What you will soon realize is that the first year of graduate school is a time of important transitions in the way you study, the way you think about mathematics, the way you think about yourself and the way you think of your professors. Below I offer some suggestions of what you can do this summer in order to be better prepared for the transition to grad school. Continue reading

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